Time Weighted rate of return concept confusion

[stuartbale1]

In questions on Time Weighted rate of return in Schweser Qbank, i have seen somewhere only price of one share is used and somewhere accumulated price of all shares is used and ending value is added to the new purchase next year.
Please clarify these concepts.

 

[studyguy18]

Time weighted rate of return is calculated by finding the compound rate of return (geometric mean). This can be done for an individual stock or a portfolio of stocks, it’s the same concept in either case.
Not quite sure what you mean about the addition of ending value… Can you post a hypothetical question as an example?

 

[StageRight]

For TWRR the amount of money in each stock doesn’t matter. I find it easiest to take the price of one stock for each period. You’ll need both the price at the end of the period as well at the beginning and any dividends paid during the period. (Find the HPR for each period)
example: stock X is worth $10 at the beginning of the year, pays dividends of $1 and is sold for $15 at the end of the year. In year 2, I buy another share of stock x for $15 (the price at the beginning of the year would be the same as the price at the end of the previous period). It pays another $1 dividend and then is sold for $17 at the end of year 2.
HPR for period 1 = (15-10+1)/10
=0.6%
HPR for period 2 = (17-15+1)/15
=0.20%
The TWRR is the geometric mean of these HPR’s.
TWRR = (Sqrt(1+0.006)(1+0.002)) -1
=0.4%
SOMEONE CORRECT ME IF I’M WRONG. I NEED TO BE CORRECTED HERE SO I DON’T GET THIS WRONG ON JUNE 4

 

[Iampossible]

Have a look at 3.2 Time Weighted Rate of Return Example 4 and Example 5 in the CFAI Curriculum.
Both excellent examples - this is about as involved as it could get.
Notice in Example 5, if non-annual holding periods add up to exactly a year (one period of four months followed by another period of 8 months) you do
(1 + HPR1) (1+HPR2) -1 to get TWR
instead of
(1+TWR) ^2 = (1+HPR1) (1+HPR2) => TWR = sqrt[ (1+HPR1)(1+HPR2)] -1 when both holding periods are years.